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On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences

Author

Listed:
  • Rajesh Kumar Mohapatra

    (Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil 626126, India)

  • Tzung-Pei Hong

    (Department of Computer Science and Information Engineering, National University of Kaohsiung, Kaohsiung 811726, Taiwan
    Department of Computer Science and Engineering, National Sun Yat-sen University, Kaohsiung 804201, Taiwan)

Abstract

This paper solves the issues of determining the number F n of fuzzy subsets of a nonempty finite set X . To solve this, this paper incorporates the equivalence relation on the collection of all fuzzy subsets of X . We derive two closed explicit formulas for F n , which is the sum of a finite series in the product of binomial numbers or the sum of k -level fuzzy subsets F n , k by introducing a classification technique. Moreover, these explicit formulas enable us to find the number of the maximal chains of crisp subsets of X . Further, this paper presents some elementary properties of F n , k and F n .

Suggested Citation

  • Rajesh Kumar Mohapatra & Tzung-Pei Hong, 2022. "On the Number of Finite Fuzzy Subsets with Analysis of Integer Sequences," Mathematics, MDPI, vol. 10(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1161-:d:786455
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    References listed on IDEAS

    as
    1. V. Murali & B. B. Makamba, 2003. "On an equivalence of fuzzy subgroups III," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-11, January.
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